Introduction
Albert Einstein famously called compound interest the "eighth wonder of the world," adding, "He who understands it, earns it... he who doesn't... pays it." But what exactly is it, and why is it so powerful?
In simple terms, compound interest is interest on interest. It's the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
The Snowball Effect
Think of compound interest like a snowball rolling down a hill. At first, it's small. But as it rolls, it picks up more snow. The bigger it gets, the more snow it picks up with each rotation. This is exactly how your money grows with compound interest.
Simple vs. Compound Interest
To understand the power of compounding, let's compare it to simple interest:
- Simple Interest: Calculated only on the principal amount. If you invest $1,000 at 5% interest, you earn $50 every year, forever.
-
Compound Interest: Calculated on the principal
plus accumulated interest. If you invest $1,000 at 5%
interest:
- Year 1: You earn $50. Balance: $1,050.
- Year 2: You earn 5% on $1,050, which is $52.50. Balance: $1,102.50.
- Year 3: You earn 5% on $1,102.50, which is $55.13. Balance: $1,157.63.
Over a few years, the difference is small. But over 20, 30, or 40 years, the difference becomes massive.
The Formula
The formula for compound interest is:
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for, in years
Key Factors That Affect Growth
- Time: This is the most important factor. The longer your money has to compound, the faster it grows. This is why starting early is crucial.
- Interest Rate: A higher rate means faster growth. Even a 1% difference can mean thousands of dollars over decades.
- Frequency: How often interest is compounded (daily, monthly, annually) affects the final amount. More frequent compounding leads to higher returns.
Conclusion
Compound interest is a powerful tool for building wealth. By understanding how it works and starting early, you can take advantage of exponential growth to reach your financial goals. Use our free calculator to see how your own investments could grow over time.